Why QC Rewards Technique Over Calculation

Quantitative Comparison (QC) questions ask you to compare Quantity A and Quantity B, not to compute an exact final value. Test-takers who fully solve both sides every time waste precious minutes; test-takers who simplify and compare directly finish faster and make fewer errors.

Quantitative Comparison (QC) প্রশ্নে Quantity A ও B-এর তুলনা করতে হয়, নির্দিষ্ট চূড়ান্ত মান বের করতে হয় না। যারা প্রতিবার সম্পূর্ণ সমাধান করেন তারা সময় নষ্ট করেন; যারা সরলীকরণ করে তুলনা করেন তারা দ্রুত ও নির্ভুলভাবে শেষ করেন।

The core method: apply the same operation (add, subtract, multiply, or divide by the same value) to both quantities simultaneously to cancel out shared terms, leaving a simpler comparison — just like solving an inequality.

মূল পদ্ধতি: উভয় রাশিতে একই ক্রিয়া প্রয়োগ করে সাধারণ পদ বাতিল করুন, তুলনা সহজ করুন।

Core Strategies

StrategyWhen to Use It
Simplify, don't fully solveCancel shared terms from both quantities using identical operations before doing any arithmetic.
Test multiple number typesWhen variables are involved with no stated constraints, test a positive integer, a negative number, a fraction, and zero — if the relationship changes, the answer is D.
Never multiply/divide by a variableIf a variable could be negative, multiplying or dividing by it can flip an inequality — avoid this until you know its sign.
Watch for "cannot be determined" being unavailableIf both quantities are specific numbers with no variables, the answer can never be D — one of A, B, or C must be correct.
Use given constraints fullyInformation like "x is a positive integer" or "0 < y < 1" often rules out the number types that would otherwise force answer D.

Worked Examples

Example 1 — Simplify First
Quantity AQuantity B
3(x + 4)3x + 8
SIMPLIFYQuantity A = 3x + 12. Subtract 3x from both quantities: Quantity A becomes 12, Quantity B becomes 8. Since 12 > 8 regardless of x's value, Quantity A is always greater (A) — no need to know x at all.
Example 2 — Test Multiple Numbers
Quantity AQuantity B
x²x

(No constraints on x are given.)

TEST NUMBER TYPESIf x = 2: A = 4, B = 2 → A greater. If x = 0.5: A = 0.25, B = 0.5 → B greater. Since the relationship flips depending on which number is used, the answer is D — cannot be determined.

Common Mistakes

  • Assuming variables are positive integers by default: unless stated, a variable can be negative, zero, or a fraction — each can change the comparison.
  • Multiplying both sides by a variable of unknown sign: this can silently flip the direction of the inequality without you noticing.
  • Choosing D when specific numbers are given: if both quantities reduce to fixed numbers with no variables, D is never the correct answer — one relationship must hold.
  • Stopping after testing only one number: a single test case that shows "A greater" doesn't rule out D; you must also test a case designed to break the pattern (negative, fraction, zero).

Your Turn

Compare each pair using simplification or number-testing. সরলীকরণ বা সংখ্যা পরীক্ষা করে প্রতিটি জোড়া তুলনা করুন।

1 Quantity A: 5x + 7  |  Quantity B: 5x + 3
Show the logic

Subtract 5x from both: A' = 7, B' = 3. A is always greater, regardless of x.

2 Given x ≠ 0. Quantity A: x²  |  Quantity B: 0
Show the logic

Any nonzero number squared is positive. A is always greater (A).

3 Quantity A: (x + 3)²  |  Quantity B: x² + 9 (no constraint on x)
Show the logic

Expand A: x² + 6x + 9. Subtract x² + 9 from both: A' = 6x, B' = 0. If x > 0, A greater; if x < 0, B greater; if x = 0, equal. Answer: D.

4 Given 0 < y < 1. Quantity A: y  |  Quantity B: y²
Show the logic

For any fraction between 0 and 1, squaring makes it smaller (e.g., 0.5² = 0.25). A is always greater (A) — the constraint rules out the number types that would otherwise force D.

5 Quantity A: the average of 12, 18, and 24  |  Quantity B: 18
Show the logic

Average = (12+18+24)/3 = 54/3 = 18. Both specific numbers, no variables — D is not possible. The two quantities are equal (C).